I recollect TWO movies called The River. One, which isn't what you want, is a great movie, in India, having a lot to do with the Ganges. But that's not it.

The second had the name The River also, I believe. It was about a young family (from Iowa?) dealing with a killer flood which engulfed their farm. A fine film.   I just could be wrong about the name, but it was something like that.

Dave Oesterreich